(NECN/NBC News: Brian Mooar) - The White House announced Sunday that it has followed through on its promise to fix the Healthcare.gov website.

After an embarrassing launch, the administration has promised to have the site working for the vast majority of people who log on and try to buy health insurance.

But even supporters concede there's still a lot of room for improvement.

The White House says it has met a self-imposed November 30 deadline to get healthcare.gov working, for the most part.

"The administration has hit the big benchmarks they set out, right? 50,000 people at one time, 800,000 people a day," said Democratic Rep. Chris Van Hollen of Maryland. "Look, this is going to take some time before it's up and kicking in full gear."

The administration promised to have the web site not completely fixed, but working for the vast majority of people trying to sign up for health care.

Republican critics, though, say the website isn't the only problem.

'So, what they've done is disrupted it for the 85 percent that had health care," said Republican Rep. Mike Rogers of Michigan. "And their costs are going up significantly. So we've broken the system to help a few.

But for those few, signing up for affordable health insurance is a liberating experience.

"I love it," said Shaun Peet of Virginia. "There were no problems."

A web expert invited to inspect the efforts to fix Healthcare.gov says it's too early to declare victory.

"The largest challenge with this site is just making sure that it stays up and running," said John Engates.

The White House describes the website as a work in progress, but dramatically better than it was when it went online October 1.

The administration says the successful enrollment rate has gone from 30 percent to 80 percent.

When the site went online, it was up only 43 percent of the time. The administration says that's now been improved to 95 percent.